Odds of Hanging On
You will have more competition but more business where hunting is popular, though the big money is actually in urban areas where the wealthy big game hunters live.
You'll increase your odds if you have a specialty or focus on a niche market. Good marketing is not easy, but is essential for growing a successful business. Only you know your customers, so you will have to be your marketing expert. A lot cheaper than hiring someone, though a good web designer can make all the difference, especially for passive income channels like eBay.
If science fiction becomes nonfiction, your job could be replaced by a 3D printer capable of reproducing models of animals. Of course, cloning could also provide a steady stream of potential taxidermy specimens.